Geometrical Studies of Complex Geological Media Using Scaling Laws

摘要

This doctoral thesis applies scaling concepts to characterize the morphology of geological porous media and fracture networks and relates scaling exponents to the sample's physical properties. The first part of the thesis applies multifractal scaling (MS) to the study of the morphology of random porous media. MS is used to characterize scanning electron microscope (SEM) images of chalk samples from the North Sea, and dipmeter micro resistivity signals from several wells in different North Sea reservoirs. The second part of the thesis develops and characterizes a model of a stochastic fracture network. Here, the application of the scaling concept differs from that in the first part, since the scaling concept is applied to percolation structures and not used as a characterization tool based on MS. Several methods and concepts must be introduced to characterize geological data and to understand the fracture model and some of them are described in four enclosed research papers. Paper 1, on the SEM images, suggests that pore space of sedimentary chalk is multifractal. Papers 2 and 3, on the dipmeter signals from reservoir wells, present a new method for extracting information about geological formations from a micro resistivity log. The main conclusion of Paper 4 on fracture networks, is that the influence of fracture shapes on percolation thresholds, block densities and topology could be explained using the concept of excluded volume. 114 refs., 48 figs., 6 tabs.